nplbin: Non-Positive Log-Binomial Regression

Description

Finds the maximum likelihood estimate of a log-link binomial GLM using an EM algorithm, where each of the coefficients in the linear predictor is restricted to be non-positive.

Usage

nplbin(y, x, offset, start, control = list())

Arguments

binomial response. May be a single column of 0/1 or two columns, giving the number of successes and failures.

non-negative covariate matrix.

offset

non-positive additive offset vector. The default is a vector of zeros.

start

starting values for the parameter estimates. All elements must be less than or equal to -control$bound.tol.

control

a logbin.control object, which controls the fitting process.

Value

coefficients: the constrained non-positive maximum likelihood estimate of the parameters.
residuals: the residuals at the MLE, that is y - fitted.values
fitted.values: the fitted mean values.
rank: the number of parameters in the model (named "rank" for compatibility --- we assume that models have full rank)
family: included for compatibility --- will always be binomial(log).
linear.predictors: the linear fit on link scale.
deviance: up to a constant, minus twice the maximised log-likelihood.
aic: a version of Akaike's An Information Criterion, minus twice the maximised log-likelihood plus twice the number of parameters.
aic.c: a small-sample corrected version of Akaike's An Information Criterion (Hurvich, Simonoff and Tsai, 1998).
null.deviance: the deviance for the null model, comparable with deviance. The null model will include the offset and an intercept.
iter: the number of iterations of the EM algorithm used.
weights: included for compatibility --- a vector of ones.
prior.weights: the number of trials associated with each binomial response.
df.residual: the residual degrees of freedom.
df.null: the residual degrees of freedom for the null model.
y: the y vector used.
converged: logical. Did the EM algorithm converge (according to conv.test)?
boundary: logical. Is the MLE on the boundary of the parameter space --- i.e. are any of the coefficients < control$bound.tol?
loglik: the maximised log-likelihood.
nn.design: the non-negative x matrix used.

Details

This is a workhorse function for logbin, and runs the EM algorithm to find the constrained non-positive MLE associated with a log-link binomial GLM. See Marschner and Gillett (2012) for full details.

References

Hurvich, C. M., J. S. Simonoff and C.-L. Tsai (1998). Smoothing parameter selection in non-parametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60(2): 271--293.

Marschner, I. C. and A. C. Gillett (2012). Relative risk regression: reliable and flexible methods for log-binomial models. Biostatistics 13(1): 179--192.